2 Answers
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The fee for transferring tokens will be in ETH, as the act of transferring tokens is done by executing a transaction on the Ethereum network. If you're transferring from an exchange to a wallet, it's up to the exchange how they handle the fee. They may just take a portion of your token, but they should specify that to you in advance.

You can store as many ERC-20 tokens in the same wallet as ether. You can access them on MyEtherWallet by specifying the token contract address (if MEW doesn't natively support VEN).

Binance (exchange I am using) charges 5 VEN for withdrawal. If I understand correctly, that is not the gas for the miner fee, am I right? In that case, do I need to have ETH in my MEW wallet?
– JakeJan 5 '18 at 5:01

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They probably cover the miner fee, then. If any ETH is required, Binance would require you to have it, not MEW. You will need ETH in your MEW wallet if you want to sent the tokens somewhere from there, though.
– KyleJan 5 '18 at 19:27

Thanks @Sean. So to send from Exchange to MEW, I just enter the public address of my wallet in Exchange. But to send from my wallet to another wallet or Exchange, I need to set up the custom token in MEW?
– JakeJan 5 '18 at 5:01